# How to write all real numbers except 0 in set notation

## How to write all real numbers in set notation

The whole real line is considered to be both open and closed. And notice, I have negative three is less than or equal to x so that's telling us that x could be equal to, that x could be equal to negative three. We think of a function that takes one number as input and spits out another number as output. Let me use a different color. For instance is the set with the three elements -1, and. Now you're probably wondering, okay, in this case both endpoints were included, it's a closed interval. An interval is said to be left-open if and only if it contains no minimum an element that is smaller than all other elements ; right-open if it contains no maximum ; and open if it has both properties. The range of f is the set of outputs it produces. I care about all the numbers from negative three to two.

And the view there is you could never include everything all the way up to infinity. Let's say this number line is showing different values for x. I'll get another number line here. Our example is written in interval notation as. The interior of an interval I is the largest open interval that is contained in I; it is also the set of points in I which are not endpoints of I.

This means all of the numbers between 3 and 5. Thus, in set builder notation.

For sets with infinitely many elements this becomes impossible, so there are other ways to write them down. We can also talk about the range of this function.

One last example.

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